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Wilson's Theorem in Disguise
The American Mathematical Monthly problem 10578 considers a sequence defined by recurrence equation with initial conditions and asks to show that is only an integer for prime .
This Demonstration uses Mathematica's built-in function RecurrenceTable to generate the sequence and finds for which is an integer.



It is easy to find a symbolic solution of the above recurrence equation:
The above fraction is an integer only for prime by virtue of Wilson's theorem.


"Wilson's Theorem in Disguise" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/WilsonsTheoremInDisguise/
Contributed by: Oleksandr Pavlyk and Brett Champion
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